PSI - Issue 36

Ivan Pidgurskyi et al. / Procedia Structural Integrity 36 (2022) 190–196 Ivan Pidgurskyi, Mykola Stashkiv, Mykola Pidgurskyi et al. / Structural Integrity Procedia 00 (2021) 000 – 000

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particularly surface cracks can be initiated. Under certain conditions, several surface cracks can occur at the same time merging as they grow and forming a major crack. The rules for coalescence of adjacent surface cracks in the calculation schemes are presented in the Codes and Standards ASME Code Sec XI, BS 7910, FITNET, APi579-1, GB/T 19624 and others. Their analysis is given in (Lu et al. (2017), Pang et al. (2017)). In particular, when assessing the fatigue crack growth life of structural elements in ASME Code Sec. XI, BS 7910 and FITNET, the calculated scheme of propagation of each of the adjacent cracks until their coalescence is considered. Then, neglecting the coalescence period of cracks, they are replaced by one equivalent surface crack of the same depth a as adjacent cracks, and with the total length on the surface 2 c 1 + 2 c 2 . Other standards are more conservative, as the design scheme for cracks coalescence involves replacing them with one larger crack with an additional gap between them. This scheme neglects not only the stage of cracks coalescence, but also the period of their mutual influence before the coalescence. An analysis of the Rules and Standards shows (Bezensek et al. (2011)) that the calculation of fatigue crack growth life of structures with surface cracks has been constantly updated in recent decades. This is explained both by the improvement of defectoscopic equipment for defect detection and their control (Sheerin Sitara et al. (2018)), as well as the development of calculation methods, in particular the finite element method (FEM) (Lin et al. (2019a), Yasniy et al. (2017)). The study of the coalescence process of surface cracks is considered in (Patel et al. (2010), Bayley et al. (1999)). It is established that when two coplanar surface cracks are combined, the major crack with a saddle-shaped front is formed. With the development of the crack, the curvature of saddle-shaped front is gradually decreases; the contour acquires a semi-elliptical shape. In (Patel et al. (2010)), a model of crack coalescence is considered, in which the idea of relative crack overlap is implemented. The major crack changes its sizes both in the coalescence zone and on the surface. The disadvantage of this model is the conjugation zone, which is modeled by the intersection of the semi-ellipses. This conjugation does not correspond to the experimental data (Bezensek et al. (2004)), especially in the final stage of coalescence. This will significantly affect the distribution of SIFs in the conjugation zone. In the second model (Bayley et al. (1999)), the process of crack coalescence is modeled by a series of contours that gradually smooth the saddle-shaped front. The conjugation zone of the semi-ellipses is modeled by the radii of concentric circles, the center of which is on the rear cross-sectional surface of the sample. It should be noted that the geometry of such a model is insufficiently substantiated. It should be noted that the process of coalescence of surface cracks is analyzed by the values of SIF in the area of the saddle-shaped front (Lin et al. (1999c)), which, in turn, significantly depend on the geometry of the cracks and their conjugation (Lin et al. (1999b)). Therefore, the aim of this study is to evaluate the influence of surface crack shape parameters on the durability of their coalescence stage and to assess the residual durability of a structural element with identical coplanar surface cracks taking into account their coalescence. 2. Research methodology Modeling of kinetics of surface cracks propagation, in particular their coalescence, was performed on 09Г2С steel samples with mechanical characteristics σ y = 380 MPa and σ u = 540 MPa and cyclic crack resistance characteristics n = 3.08 and C = 8.9·10 -12 MPa -n · m 1-n/2 of medium-amplitude section of crack growth rate versus the stress intensity factor range (da /dN vs. ΔK ) curve. Samples with a cross-section of 80 x 20 mm under cyclic tensile loading with maximum cycle stresses σ n = 150 MPa and 187.5 MPa and stress ratio R = 0 and 0.25, respectively, were modeled. The scheme by which the survivability of the structural element N coal was evaluated taking into account the stage of coalescence is presented in Fig. 1. Also the approach for estimating the residual durability of N crack , which is proposed by the Rules of the American Society of Mechanical Engineers (ASME) (ASME (2005)), Standard BS 7910 (BS7910 (2013)), FITNET is presented. In this calculation scheme, two cracks at the contact moment are replaced by an equivalent crack of the same depth a . In this case, the coalescence period of cracks N coal is neglected.